 Here \(H_0\)  is the Hamiltonian of undisturbed atom with \(\Omega \)  being the spectral distance between ground and excited multiplets. The second term in the expression for \(H_0\)  describe Zeeman splitting with \(\omega _{iL}\)  being Larmor frequencies of \(i\) -th multiplet (\(i=1\)  refers to the ground state and \(i=2\)  the excited state). Term \(H_E\)  describe the action of monochromatic \(\sim e^{-\imath \omega t}\)  electromagnetic field of the probe beam which is linearly polarised in \(ZX\)  plain. The quantities \(\omega _{x,z}\)  correspond to Rabi frequencies defined by the dipole moment \(d\)  of optical transition between the ground and excited multiplets and by the amplitudes \(A_{0x,z}\)  of electric field projections of the probe beam at point \(\bf R\)  where the atom is located: \(\omega _{i}\equiv dA_{0i}({\bf R})/ \hbar , i=x,z\) .
Each `element' of matrices in Eq. (REF ) is itself a matrix with dimensions \((2F+1)\times (2F+1)\) , with \(J_z\)  and \(J_x\)  being known matrices of the corresponding projections of the angular momentum \(F\)  [1]}.
The matrices of the operators for the needed \(x\)  and \(z\)  projections of the atomic dipole moment have the form
\(d_x\equiv d \begin{pmatrix} 0 & J_x \\ J_x & 0 \end{pmatrix}, \quad d_z\equiv d \begin{pmatrix} 0 & J_z \\ J_z & 0 \end{pmatrix}.\) 
